In optical communications, as a data rate of the optical communication increases, complicated modulation formats such as quadrature-amplitude modulation (QAM) formats including 8QAM, 16QAM, 64QAM, 256QAM, 1024QAM, etc., are used because sufficient Euclidian distances are designed. However, these modulation formats typically cause signal power variations depending on the symbols, and can cause phase noise on the signal of the channel as well as other wavelength-division multiplexed channels through the optical fiber nonlinearity. Phase-shift keying (PSK) modulation formats offer constant modulus which provide a constant signal power at each symbol timing. However, the PSK modulation formats show a poor performance regarding the higher bit-error rate (BER) compared to the QAM formats, because the PSK modulation formats are based on shorter Euclidian distances than those of the QAM formats.
If certain properties of the QAM formats and the PSK modulation formats are properly combined and applied without losing their advantages, it would result in the lower BER, higher data rates, longer fiber distance and the higher spectral density. Accordingly, other coded modulation schemes, which provide sufficient Euclidian distances with less signal power variations per symbols, are required.